This complexity is optimal, due to a lower bound of \(\tilde{\Omega }(n^{1-2/p})\)  rounds by Fischer, Gonen, Kuhn, and Oshman [1]}, which generalizes the aforementioned lower bound for triangle listing of [2]} and [3]}, using additional machinery. In the \(\mathsf {BROADCAST~CONGESTED~CLIQUE}\)  model, Drucker, Kuhn, and Oshman [4]} show that \(\Omega (n/\log {n})\)  rounds are needed for \(p\) -cliques, even for the stronger detection variant, for almost all values of \(p\ge 4\)  (as long as \(p\le (1-\epsilon )n\)  for some constant \(\epsilon >0\) ).
